Impact of parameter variability and environmental noise on the Klausmeier model of vegetation pattern formation
type: Item
instance of: scholarly article
title: Impact of parameter variability and environmental noise on the Klausmeier model of vegetation pattern formation
zbMATH Open document ID: 1390.93122
author: Merlin C. Köhnke
author: H. Malchow
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: Semi-arid ecosystems made up of patterned vegetation, for instance, are thought to be highly sensitive. This highlights the importance of understanding the dynamics of the formation of vegetation patterns. The most renowned mathematical model describing such pattern formation consists of two partial differential equations and is often referred to as the Klausmeier model. This paper provides analytical and numerical investigations regarding the influence of different parameters, including the so-far not contemplated evaporation, on the long-term model results. Another focus is set on the influence of different initial conditions and on environmental noise, which has been added to the model. It is shown that patterning is beneficial for semi-arid ecosystems, that is, vegetation is present for a broader parameter range. Both parameter variability and environmental noise have only minor impacts on the model results. Increasing mortality has a high, nonlinear impact underlining the importance of further studies in order to gain a sufficient understanding allowing for suitable management strategies of this natural phenomenon.
Mathematics Subject Classification ID: 93A30
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 92C80
zbMATH DE Number: 6898698
zbMATH Keywords: Klausmeier model
zbMATH Keywords: pattern formation
zbMATH Keywords: self-organization
zbMATH Keywords: reaction-diffusion-advection model
zbMATH Keywords: environmental noise
describes a project that uses: TikZ
describes a project that uses: XPPAUT
describes a project that uses: pgf
MaRDI profile type: Publication
full work available at URL: math5040069
OpenAlex ID: W2768284727
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DOI: 10.3390/MATH5040069
description: scientific article; zbMATH DE number 6898698